diving deeper into the common core state standards for … · 2011-04-01 · today’s webinar will...
TRANSCRIPT
Today’s Webinar will begin shortly
Diving Deeper into the Common Core State Standards for Mathematics:
Leading with the Mathematical Practices
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deeper-dive-into-the-common-core-mathematical-standards/
National Council of Supervisors of Mathematics
Diving Deeper into the Common Core State Standards for
Mathematics:Leading with the
Mathematical Practices
www.mathedleadership.org
3A recording of today’s webinar will be available at:
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Presenters
Diane J. Briars, NCSM President
Valerie Mills, NCSM Central 1 Regional Director
Suzanne Mitchell, NCSM President-Elect
The critical first steps will be to help educators interpret and understand the CCSS and to support
the development and implementation of comprehensive, coherent instruction and
assessment systems… we plan to work with our local, state, and national affiliates to feature the
CCSS in our professional development opportunities, including annual and regional
conferences, academies, and seminars…
NCSM Joint Public Statement with NCTM, AMTE and ASSM, June 2010
5A recording of today’s webinar will be available at:
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Today’s Goals
• Provide a close look at the Standards for Mathematical Practices
• Consider how you can support student engagement in the mathematical practices through your mathematics program.
6A recording of today’s webinar will be available at:
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What is NCSM?
International organization of and for mathematics education leaders:
Coaches and mentorsCurriculum leadersDepartment chairsDistrict supervisors/leadersMathematics consultantsMathematics supervisorsPrincipalsProfessional developers
Publishers and authorsSpecialists and coordinatorsState and provincial directorsSuperintendentsTeachersTeacher educatorsTeacher leaders
7A recording of today’s webinar will be available at:
http://www.carnegielearning.com/webinars http://www.mathedleadership.org/events/webinars.html
Common Core State Standards for Mathematics
Two types of standards:• Content Standards• Standards for Mathematical Practice
Please have a copy of the Standards for Mathematical Practice.They are in the webinar handout at
http://www.carnegielearning.com/webinars/deeper-dive-into-the-common-core-mathematical-standards/
8A recording of today’s webinar will be available at:
http://www.carnegielearning.com/webinars http://www.mathedleadership.org/events/webinars.html
Standards for Mathematical Practice
“The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education.”(CCSS, 2010)
9A recording of today’s webinar will be available at:
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Underlying Frameworks
National Council of Teachers of Mathematics
5 Process Standards• Problem Solving• Reasoning and Proof• Communication• Connections• Representations
NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: Author.
10A recording of today’s webinar will be available at:
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Underlying Frameworks
Strands of Mathematical Proficiency
Strategic Competence
Adaptive Reasoning
Conceptual Understanding
Productive Disposition
Procedural Fluency
NRC (2001). Adding It Up. Washington, D.C.: National Academies Press.
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• Conceptual Understanding – comprehension of mathematical concepts, operations, and relations
• Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
• Strategic Competence – ability to formulate, represent, and solve mathematical problems
• Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification
• Productive Disposition – habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.
Strands of Mathematical Proficiency
12A recording of today’s webinar will be available at:
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Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the
reasoning of others.4. Model with mathematics. 5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated
reasoning.
13A recording of today’s webinar will be available at:
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The Standards for Mathematical Practice
Take a moment to examine the first three words of each of the 8 mathematical
practices… what do you notice?
Mathematically Proficient Students…
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The Standards for [Student] Mathematical Practice
Consider the verbs that illustrate the student actions each practice.
For example, examine Practice #3: Construct viable arguments and critique the reasoning of
others.Highlight the verbs.
Discuss with a partner: What jumps out at you?
15A recording of today’s webinar will be available at:
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Mathematical Practice #3: Construct viable arguments and critique the reasoning of others
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
16A recording of today’s webinar will be available at:
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Mathematical Practice #3: Construct viable arguments and critique the reasoning of others
Mathematically proficient students:• understand and use stated assumptions, definitions, and previously established results in
constructing arguments. • make conjectures and build a logical progression of statements to explore the truth of their
conjectures. • analyze situations by breaking them into cases, and can recognize and use counterexamples. • justify their conclusions, communicate them to others, and respond to the arguments of others. • reason inductively about data, making plausible arguments that take into account the context
from which the data arose. • compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning
from that which is flawed, and-if there is a flaw in an argument-explain what it is. • construct arguments using concrete referents such as objects, drawings, diagrams, and actions.
Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades.
• determine domains to which an argument applies. • listen or read the arguments of others, decide whether they make sense, and ask useful
questions to clarify or improve the arguments.
17A recording of today’s webinar will be available at:
http://www.carnegielearning.com/webinars http://www.mathedleadership.org/events/webinars.html
Mathematical Practice #3: Construct viable arguments and critique the reasoning of others
Mathematically proficient students:• understand and use stated assumptions, definitions, and previously established results in
constructing arguments. • make conjectures and build a logical progression of statements to explore the truth of their
conjectures. • analyze situations by breaking them into cases, and can recognize and use counterexamples. • justify their conclusions, communicate them to others, and respond to the arguments of others. • reason inductively about data, making plausible arguments that take into account the context
from which the data arose. • compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning
from that which is flawed, and-if there is a flaw in an argument-explain what it is. • construct arguments using concrete referents such as objects, drawings, diagrams, and actions.
Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades.
• determine domains to which an argument applies. • listen or read the arguments of others, decide whether they make sense, and ask useful
questions to clarify or improve the arguments.
18A recording of today’s webinar will be available at:
http://www.carnegielearning.com/webinars http://www.mathedleadership.org/events/webinars.html
The Standards for [Student] Mathematical Practice
On a scale of 1 (low) to 6 (high), to what extent is your school/district promoting
students’ proficiency in Practice 3?Evidence for your rating?
19A recording of today’s webinar will be available at:
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The Standards for [Student] Mathematical Practice
SMP1: Explain and make conjectures…SMP2: Make sense of…SMP3: Understand and use…SMP4: Apply and interpret…SMP5: Consider and detect…SMP6: Communicate precisely to others…SMP7: Discern and recognize…SMP8: Notice and pay attention to…
20A recording of today’s webinar will be available at:
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Standards for Mathematical Practice
• Describe the thinking processes, habits of mind and dispositions that students need to develop a deep, flexible, and enduring understanding of mathematics; in this sense they are also a means to an end. SP1. Make sense of problems
“….they [students] analyze givens, constraints, relationships and goals. ….they monitor and evaluate their progress and change course if necessary. …. and they continually ask themselves “Does this make sense?”
21A recording of today’s webinar will be available at:
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Standards for Mathematical PracticeAND….
• Describe mathematical content students need to learn. SP1. Make sense of problems
“……. students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends.”
22A recording of today’s webinar will be available at:
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Buttons TaskGita plays with her grandmother’s collection of black & white buttons. She arranges them in patterns. Her first 3 patterns are shown below.
Pattern #1 Pattern #2 Pattern #3 Pattern #4
1. Draw pattern 4 next to pattern 3.2. How many white buttons does Gita need for Pattern 5 and Pattern
6? Explain how you figured this out.3. How many buttons in all does Gita need to make Pattern 11?
Explain how you figured this out.4. Gita thinks she needs 69 buttons in all to make Pattern 24. How
do you know that she is not correct?How many buttons does she need to make Pattern 24?
23A recording of today’s webinar will be available at:
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Button Task
1. Individually complete parts 1 - 3.
2. Then work with a partner to compare your work and complete part 4. (Look for as many ways to solve parts 3 and 4 as possible.)
24A recording of today’s webinar will be available at:
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Buttons Task-SolutionsGita plays with her grandmother’s collection of black & white buttons. She arranges them in patterns. Her first 3 patterns are shown below.
Pattern #1 Pattern #2 Pattern #3 Pattern #4
1. Draw pattern 4 next to pattern 3.2. How many white buttons does Gita need for Pattern 5 and Pattern 6? Explain how
you figured this out. 15 buttons and 18 buttons3. How many buttons in all does Gita need to make Pattern 11? Explain how you
figured this out. 34 buttons4. Gita thinks she needs 69 buttons in all to make Pattern 24. How do you know that
she is not correct?
How many buttons does she need to make Pattern 24? 73 buttons
25A recording of today’s webinar will be available at:
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Buttons TaskHow many buttons in all does Gita need to make Pattern 11? Explain how you figured this out.
Pattern #1 Pattern #2 Pattern #3 Pattern #11
• 3+3+3+3+3+3+3+3+3+3+3+1 • 11 groups of 3 plus 1 • (11 x 3) + 1
• 11 + 11 + 11 + 1 • 3 groups of 11 plus 1• 3 x 11 + 1
26A recording of today’s webinar will be available at:
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Button Task
Which mathematical practices are needed complete the task?
Indicate the primary practice.1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of
others.4. Model with mathematics. 5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.
27A recording of today’s webinar will be available at:
http://www.carnegielearning.com/webinars http://www.mathedleadership.org/events/webinars.html
Standards for [Student] Mathematical Practice
“Not all tasks are created equal, and different tasks will provoke different levels and kinds
of student thinking.”Stein, Smith, Henningsen, & Silver, 2000
“The level and kind of thinking in which students engage determines what they will learn.”
Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human, 1997
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The Nature of Tasks Used in the Classroom …
Tasks as they appear in curricularmaterials Student
learning
Will Impact Student Learning!
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But, WHAT TEACHERS DO with the tasks matters too!
Stein, Grover & Henningsen (1996)Smith & Stein (1998)Stein, Smith, Henningsen & Silver (2000)
The Mathematical Tasks Framework
Tasks as set up by teachers
Tasks as they
appear in
curricular materials
Tasks as enacted
byteachers
andstudents
Studentlearning
30A recording of today’s webinar will be available at:
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www.Inside Mathematics.org
• http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-numerical-patterning/218-numerical-patterning-lesson-planning?phpMyAdmin=NqJS1x3gaJqDM-1-8LXtX3WJ4e8
A reengagementlesson using the Button Task
Francis DickinsonSan Carlos ElementaryGrade 5
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Learner A
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Learner B
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Button Task Revisited• What might a teacher get out of using the same
math task two days in a row, rather than switching to a different task(s)?– Address common misconceptions
– Support students in moving from less to more sophisticated solutions
34A recording of today’s webinar will be available at:
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Button Task RevisitedWhich of the Standards of Mathematical Practice did the
students engage in when they revisited the task?Indicate the primary practice.
1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of
others.4. Model with mathematics. 5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.
35A recording of today’s webinar will be available at:
http://www.carnegielearning.com/webinars http://www.mathedleadership.org/events/webinars.html
But, WHAT TEACHERS DO with the tasks matters too!
Stein, Grover & Henningsen (1996)Smith & Stein (1998)Stein, Smith, Henningsen & Silver (2000)
The Mathematical Tasks Framework
Tasks as set up by teachers
Tasks as they
appear in
curricular materials
Tasks as enacted
byteachers
andstudents
Studentlearning
36A recording of today’s webinar will be available at:
http://www.carnegielearning.com/webinars http://www.mathedleadership.org/events/webinars.html
Triangles Task
In triangle ABC, the point P is one third of the way from Ato B.
1. Explain why the area of the shaded triangle is 2/3 of the area of triangle ABC.
Source: Insidemathematics.org: MARS, 2008
37A recording of today’s webinar will be available at:
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Triangles Task
Two new points, Q and R, have been added to triangle ABC. Q is one third of the way form B to C and R is one third of the way
from C to A.
2. Explain why the area of shaded triangle PBQ is 1/3 of 2/3 of the area of triangle ABC.
Source: Insidemathematics.org: MARS, 2008
38A recording of today’s webinar will be available at:
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Standards for [Student] Mathematical Practice
The 8 Standards for Mathematical Practice –place an emphasis on student demonstrations
of learning…Equity begins with an understanding of how
the selection of tasks, the assessment of tasks, the student learning environment creates great
inequity in our schools…
39A recording of today’s webinar will be available at:
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Implementation Issue
To what extent do all students in your class, school or district have the
opportunity to engage in tasks that promote attainment of the mathematical
practices on a regular basis?Please rate on a scale of
1 (low) to 6 (high).
40A recording of today’s webinar will be available at:
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Leading with the Mathematical Practices
• Build upon/extend work on NCTM Processes and NRC Proficiencies
• Phase in implementation• Consider relationships among the
practices• Analyze instructional tasks in terms of
opportunities for students to regularly engage in practices.
41A recording of today’s webinar will be available at:
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Insidemathematics.org
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Insidemathematics.org
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Forthcoming Resources and ToolsNCSM
• Illustrating the Standards for Mathematical Practice professional development materials.
– NCSM Annual Conference session
• Tool for analyzing instructional materials in light of CCSS and related professional development activities.
– Under development in collaboration with Bill Bush, University of Louisville, and CCSSO.
– Target release date: June 1, 2011.
44A recording of today’s webinar will be available at:
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AMTE, ASSM, NCSM, NCTMPriority Activities
1. Advancing the Vision of High Quality Mathematics Education: Supporting Implementation of CCSS.
a. Toolkit b. Regional meetings of leadership teams
2. Appoint a Joint Committee of AMTE, ASSM, NCSM and NCTM to serve as an ongoing advisory group regarding CCSS.
3. Convene a panel of professional development experts to develop a conceptual framework for teacher professional development systems to support CCSS at the school, district and state levels.
45A recording of today’s webinar will be available at:
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AMTE, ASSM, NCSM, NCTMPriority Activities
4. Convene an Assessment Working Group to coordinate the field’s best guidance on assessment development and ensure that new student assessments address the priorities (e.g., mathematical practices) articulated in CCSS.
5. Develop and launch a research agenda focused on implementation of the CCSS that includes systematic study of the instantiation and implementation of the standards, monitors the impact on instruction and student learning and informs revisions of CCSS.
46A recording of today’s webinar will be available at:
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Forthcoming CCSS Companion Resources
• Technical Manual– Highlights structural features in the
standards but not highly visible, e.g., how particular ideas connect and grow across grades.
• Standards Progressions documents
47A recording of today’s webinar will be available at:
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The Illustrative Mathematics Project
• Will develop a complete set of tasks for each standard– Range of difficulty– Simple illustrations of single standards to complex
tasks spanning many standards.
• Provide a process for submitting, discussing, reviewing, and publishing tasks.
• Launch Team: Phil Daro, William McCallum (chair), Jason Zimba
illustrativemathematics.org
48A recording of today’s webinar will be available at:
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NCSM Professional Development Opportunities
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NCSM Professional Development Opportunities
• NCSM Summer Leadership Academy– June 21-23, 2011, Atlanta, GA
• Fall One-Day Seminars– October 19, 2011, Atlantic City– October 26, 2011, St. Louis– November 2, 2011, Albuquerque
Mathedleadership.org
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Reflection: Now What?
What actions will you take based on what we discussed today?
– What do you need to learn?– Who will you work with?– What do you need to integrate into your
practice?– Who will support you?
52A recording of today’s webinar will be available at:
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Additional questions? Contact:Diane Briars: [email protected]
Valerie Mills: [email protected] Mitchell: [email protected]
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